Computational multiscale modeling of carbon nanotube-reinforced polymers

Mohammad Silani, Timon Rabczuk, Xiaoying Zhuang

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter provides an overview on multiscale approaches applied to carbon nanotube-reinforced polymers (CNRPs). Multiscale methods can be classified into hierarchical or sequential multiscale methods, semiconcurrent multiscale methods, and concurrent multiscale methods. Hierarchical multiscale methods transfer information only from the fine scale to the coarse scale. Classical approaches are computational homogenization or the Cauchy-Born rule; the latter one is usually based on a periodic structure and hence not applicable for CNRPs. In semiconcurrent multiscale methods, information is transferred also back from the coarse scale to the fine scale during the course of the simulation. They seem computationally more feasible for nonlinear responses, as they account only for states that actually occur in the simulation. Many semiconcurrent multiscale methods, such as the FE2 approach are based on representative volume elements. In concurrent multiscale methods, the fine scale is directly embedded into the coarse scale. Many interesting results predicting mechanical, thermal, electrical, or chemical properties of CNRPs have been studied with hierarchical multiscale approaches. Far less work on the more complex semiconcurrent or concurrent multiscale methods for CNRPs in turn can be found in the literature. However, these methods promise to address many unresolved aspects, such as fracture.

Original languageEnglish
Title of host publicationCarbon Nanotube-Reinforced Polymers
Subtitle of host publicationFrom Nanoscale to Macroscale
PublisherElsevier Inc.
Number of pages13
ISBN (Electronic)9780323482226
ISBN (Print)9780323482219
Publication statusPublished - 2018


  • Carbon nanotube-reinforced polymers (CNRPs)
  • Cauchy-Born rule
  • Concurrent multiscale methods
  • Handshake coupling methods
  • Hierarchical multiscale methods
  • Semiconcurrent multiscale methods

ASJC Scopus subject areas

  • General Chemistry


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